What is the diameter for this given equation? (x^2+24) + (y^2+4y) = 85

The answer to your question is 2√233 ≈ 30.5

Step-by-step explanation:

Data

(x² + 24x) + (y² + 4y) = 85

Process

1. - Complete the perfect square trinomials

(x² + 24x + (12) ²) + (y² + 4y + (2) ²) = 85 + 12² + 2²

2. - Simplify

(x² + 24x + 144) + (y² + 4y + 4) = 85 + 144 + 4

(x + 12) ² + (y + 2) ² = 233

3. - Calculate the radius

radius² = 233

radius = √233

diameter = 2radius

diameter = 2√233 ≈ 30.5